In brief the problem can be stated as follows:

Given dependent variables Q_i i=1,...,N and independent variables x_i, y_i, and z_i i=1,...,N

which are related via the following system of N linear equations with parameters P₁, P₂ and P₃ :

Q_i = P₁x_i+P₂y_i+P₃z_i   i=1,...,N

How to find the optimal values of  P₁, P₂ and P₃ which satisfy the above system of linear equations subject to the following constraints:

P_i>=0   i=1,2,3

and  P₁>=P₂P₃

 Without the requirement of P₁>=P₂P_3, the problem can be solved with the Non-negative Least Squares Method of Lawson and Hanson.  But with this additional constraint, I am stuck.  

Your suggestions are welcome.